Determine if F(n.y,z) =x+y+Z have a maximum/minimum value when m,9, z) lies on unit sphere:x'+yiZ=1• 2 2 2 In which Case, determine maxımum & mirimum Values·

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: A fluid has density 1200 kg/m and flows with velocity = i + yj + zk, where x, y, and z are measured…

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Q: Obtain the DE based on given conditions solve for item 1 only.

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Q: Determine the solid bounded by the surfaces 9x2+4y2=30 and the plane 9x+4y−6z=0 in the first octant.

A: Given surface is 9x2+4y2=30 and plane is  9x+4y-6z=0 Bounded region in first octane ⇒x≥0, y≥0, z≥0…

Q: Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0). (x, y, z) (smaller…

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Q: Use Lagrange multipliers to find the highest point on the curve of intersection of the surfaces.…

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Q: A fluid has density 1000 kg/m³ and flows with velocity = ci +yj + zk, where x, y, and z are measured…

A: We have to find the rate flow outward through the part of paraboloid . We can to use the methods of…

Q: 6. Where does the tangent line to r = at the point (1, 0, 1) intersect the y-z plane.

A: Given:

Q: Find the points on the cone  z2 = x2 + y2  that are closest to the point  (2, 2, 0).   (x, y, z)…

A: Given,

Q: 2. Calculate the centroid of the thin plate R which bounded by a = 1, y = 0 and, x² + y² = 4.

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Q: Q. No. 4 Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y =…

A: Given lines are, y=x and y=2-x

Q: Find the maximum volume of a rectangular box with faces parallel to the coordinate planes if one…

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Q: 1. Find the minimum distance from the point (0, 0, 0) to the plane x- y+z = 3.

A: perpendicular distance

Q: The tangent plane and the normal line of the surface y = x² + z – 6 at the point (2, -1, 1) have the…

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Q: 55. A point moves along the intersection of the elliptic parab- oloid z = x+ 3y and the plane y = 1.…

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Q: Determine the maximum highest point (x, y,=) the surface on z = 1+ 4x + 4y- x* - y*

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Q: A solid cube, 2 units on a side, is bounded by the planes x = +-1, z = +-1, y = 3, and y = 5. Find…

A: Given:

Q: Integrate ƒ(x, y, z) = x - 3y2 + z over the line segment C joining the origin to the point (1, 1, 1)

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Q: A solid “trough” of constant density is bounded below by the surface z = 4y2, above by the plane z =…

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Q: A point moves along the intersection of the elliptic paraboloid z = x + 3y² and the plane y = 3. At…

A: z=x2+3y2 and y=3 Point of Intersection : Curve z:x2+3y2=x2+3(3)2=x2+27 dzdx=2x+0 =2x

Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: Find the points on the sphere x2+y +z = 109 where f(x,y,z) = 6x + 8y + 3z has its maximum and…

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Q: Find a formula for a functionf(x, y, z) whose level surface f= 3 is a cylinder of radius 5 centered…

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Q: Find the minimum distance from the point (−2, −2, 0) to the surface                     z = √(1 − 2x…

A: We have to find the minimum distance from the point (-2,-2,0) to thesurface z=1-2x-2y

Q: 1. A such that the difference in distances between (x, y) and two fixed points (called is the set of…

A: A___ is the set of points (x, y) in a plane such that the difference in distances between (x, y) and…

Q: The diagram shows a small block B, of mass 0.2kg, and a particle P, of mass 0.5kg, which are…

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Q: Find the points on the cone z2 = x2 + y2 that are closest to the point (8, 2, 0). (x, y, z) =…

A: Here we use partial derivatives to solve this problem.

Q: Find the maximum volume of a box inscribed in the tetrahedron bounded by the coordinate planes and…

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Q: 9. Determine the position of the centroid of a sheet of metal formed by the curve y = 4x - x² which…

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Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: The tangent plane to the elliptic paraboloid z = 2x2 + y² at the point (1, 1, 3) is %3D 1) 8x + 6y +…

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Q: 2. For the surface z = In(y+ Vx² + y²). (b) Find the linear approximation at the point (3,-4).

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Q: Find the points on the sphere with center at the point P-(3,3,3) of radius 3 where the function f(x,…

A: Using Lagrange multiply method

Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

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Q: 1_2 Can you please help me with this example in a step by step guide. Thank you very much!!

A: To calculate the coordinates (x,y,z) and also define the absolute extremum for the provided surface…

Q: 4. What is the maximum value of f(x, y, z) = xyz for points (x, y, z) lying on the ellipsoid x² + 4…

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Q: B) Determine the parametrizations of the untrimmed surfaces S1, S2 and S3 without constraints(free)…

A: Given: Surfaces S1: 2x-4y+z=4 S2: 2y=6-x S3: x2=16-4z To find: Parametrization of the surfaces S1,…

Q: 7. Find the flux of F(x, y, z) = x î+ y ĵ+ z² k across the sphere of radius 1 centered at the origin…

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Q: 22 Find the Directional Derivabive of Pary,z)= xg-y2'+Z at the point CI, -2, 0) in the direcbion of…

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Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y = x and y =…

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Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x2 + y2 + z2 = 1 is T =…

A: We have given; The temperature T at any point (x, y, z) in space isT = 400xyz2and the unit spherex2…

Q: Find the minimum distance from the cone z = √(x2 + y2) to the point (-6, 4, 0).

A: To find the minimum distance

Q: Suppose that the Celsius temperature at the point (x,y,z) on the sphere x +y +z =1 is T= 1600xyz“.…

A: This is a problem related to maxima and minima. Based on the general formula we will answer the…

Q: The minimum value of f(x,y,z) = x^2 -2y + 2z^2 on the sphere x^2 + y^2 + z^2 =1 is ....?

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Q: Use Lagrange multipliers to find the minimum distance from the curve or surface Cone: z = √x2 + y2…

A: The surface of the cone               z=x2+y2 or z2-x2-y2=0                                (1)…

Q: A fluid has density 1200 kg/m³ and flows with velocity v = xi + yj + zk, where x, y, and z are…

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Q: Find the minimum distance from the cone z= to the point (6, 6, 0).

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